Problem: Rewrite as a simplified fraction. ${3.91\overline{7} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 3917.7777...\\ 100x &= 391.7777...\end{align*}}$ Subtracting the two equations, we have: ${900x = 3526}$ ${x = \dfrac{3526}{900}} $ ${x = \dfrac{1763}{450}} \text{or} {3 \dfrac{413}{450}}$